Pure fluid passive square function generator

ABSTRACT

A fluidic circuit, the output signal of which is proportional to the square of the input signal supplied thereto. The circuit comprises means for supplying an input signal and means for taking an output pressure signal proportional to the pressure of the input signal. Generation of a pressure output proportional to the square of the input pressure signal is accomplished by impacting a jet of fluid emanating from a linear resistor onto another linear resistor or a stagnation plenum. The stagnated pressure is a function of the square of the input pressure.

' United States Patent [191 Drzewiecki [4 1 May 27, 1975 PURE FLUIDPASSIVE SQUARE FUNCTION GENERATOR 3,595,258 7/1971 Kinnel 137/842Primary Examiner-William R. Cline Attorney, Agent, or FirmNathanEdelberg; Robert P.

Gibson; Saul Elbaum [57] ABSTRACT A fluidic circuit, the output signalof which is proportional to the square of the input signal suppliedthereto. The circuit comprises means for supplying an input signal andmeans for taking an output pressure signal proportional to the pressureof the input signal. Generation of a pressure output proportional to thesquare of the input pressure signal is accomplished by impacting a jetof fluid emanating from a linear resistor onto another linear resistoror a stagnation plenum. The stagnated pressure is a function of thesquare of the input pressure.

6 Claims, 5 Drawing Figures 'lOOL PURE FLUID PASSIVE SQUARE FUNCTIONGENERATOR RIGHTS OF THE GOVERNMENT The invention described herein may bemanufactured, used, and licensed by or for the United States Governmentfor governmental purposes without the payment to the inventor of anyroyality thereon.

BACKGROUND OF THE INVENTION 1. Field of the Invention This inventionrelates to pure fluid systems in general and, more specifically, to apure fluid system capable of producing a fluid pressure output signalthat is directly proportional to the square of the pressure of the fluidinput signal supplied to the system.

2. Description of the Prior Art Any computational circuit, of an analognature, generally requires a squaring capability. This is especiallytrue in the case of analog flueric computational circuits.

In the past, analog flueric computations of squares of a particularinput function have been done by complicated networks of amplifier andfeedback loops. This is amply illustrated in US. Pat. No. 3,459,206entitled Statistical Device, issued to Dexter.

The use of amplifier feedback loops is costly and complicated. By takingadvantage of the natural fluidic non-linearity of a stagnating flow ofsimple passive circuit can be constructed that can approximate, to afairly good degree, the square function. The closest prior art to theinvention of the applicant is Colston, Pure Fluid Function GeneratingSystem, US. Pat. No. 3,250,469. Colston obtains his square function intwo fundamentally different ways. These are:

l. Feeding an input pressure source through a capillary or linearresistor connected in series to an orifice which is connected toambient; the output pressure which is proportional to the square of theinput pres sure is taken from the junction between the linear resistorand the orifice; and

2. By passing the input pressure source through a linear resistor orcapillary and utilizing the output pressure of the capillary as a squarefunction of the input pressure.

An important aspect of this invention is the discovery that if a linearresistor is subjected to a pressure and grounded or connected toambient, and the resulting flow is then stagnated, the stagnationpressure will be proportional to the square of the pressure driving theresistor.

It is therefore an object of this invention to provide a pure fluidsquare function generator which utilizes the stagnated flow from alinear resistor to produce a stagnation pressure proportional to thesquare of the pressure driving the resistor.

In addition, it is an object of this invention to provide a pure fluidactive square function generator which enables power to be drawn offfrom the circuit producing the square function, that power beingproportional to the square in pressure of the input function or source.

These and other objects of the present invention will become more fullyapparent with reference to the following specifications and drawingswhich relate to two preferred embodiments of the present invention.

SUMMARY OF THE INVENTION In accordance with the disclosure hereinpresented this invention provides a pure fluid square function generatorwhich comprises a series combination of a linear resistor having a fluidsource and means for catching and stagnating the emitted jet from saidresistor, and wherein said means comprises a stagnation plenum connectedto the catcher and having an output port for measurement of the pressureat said plenum. A modification of the generator is provided so thatpower may be withdrawn with a pressure proportional to the square of theinput source pressure. This means comprises two linear resistorsconnected in series one end of which is grounded to ambient and theother end of which acts as a catcher and stagnation plenum.

BRIEF DESCRIPTION OF THE DRAWINGS The specific nature of the inventionas well as other objects, aspects, uses, and advantages thereof willclearly appear from the following decription and from the accompanyingdrawings in which:

FIG. 1a is a diagrammatic sketch of the pure fluid passive squarefunction generator.

FIG. 1b is a cross sectional view of a specific model of the pure fluidpassive square function generator.

FIG. 10 is end view of the illustration of FIG. 1b.

FIG. 1d is a graph of the output function versus the input pressure forthe pure fluid passive square function generator.

FIG. 2 is a diagramatic sketch of the pure fluid active square functiongenerator.

DESCRIPTION OF THE PREFERRED EMBODIMENTS The invention disclosed hereinmay be understood with respect to its broad aspects by reference firstto FIG. 1a where there is shown a diagrammatic view of an embodiment ofthe invention encompassing the pure fluid passive square functiongenerator. For this particular circuit the input pressure P may berelated to the output pressure P by the following equation:

where p is the density of the fluid.

A is the area of the capillary (linear resistor).

R is the resistance to the flow of the capillary.

This equation may be derived as follows: Let Q represent the flow offluid through the linear resistor of resistance R. Then, since thelinear resistor is vented to ambient 13, the pressure in the resistor isHowever, P may be assumed equal to zero since it is the ambientpressure.

If we consider the pressure of the jet 10 exiting from the linearresistor R to be P and the pressure entering the catcher 9 to be P andwrite Bernoullis equation between the exit from the linear resistor andthe catcher 11, we obtain where v is the velocity of the fluid as itexits the linear resistor, and v is the velocity of the fluid at the endof the catcher 9 in the stagnation plenum 11. However, since v is thevelocity of the fluid in the stagnation plenum 11, it characteristicallymust be zero. Hence solving Bernoullis equation v V 2P /p. Havingpreviously asserted that the flow Q P /R, we now assert VA Q and for aparabolic profile if /2 v where \7 is the average velocity of the fluidwithin the jet 10 issuing from the resistor R. Returning to our solutionof Bernoullis equation and substituting for v in terms of R, A, and P weobtain the above declared equation relating to P to P.,.

The second embodiment of the invention comprising a pure fluid activesquare function generator may best be understood by reference to FIG. 2wherein there is shown a diagramatic circuit of the invention. In thisparticular embodiment of the invention, the output pressure P isproportonal to the square of the input pressure P., by a differentconstant. The equation may also be derived from application ofBernoullis equation. Specifically, in the embodiment:

In order to draw power, the jet 16 vented to the ambient 14 is receivedby linear resistor R Resistor R is series connected to linear resistor RResistor R is vented to ambient 15. Power is drawn from between resistorR as output pressure P Reference is now made to FIG. 1b and FIG.whereion there is illustrated a specific working model of the invention.In this embodiment, fluid enters through the input port 20 and travelsalong the linear resistor with the flow therefrom impinging upon thecatcher opening 31. Fluid entering the catcher opening 31 travels alongthe catcher tube 32 and enters or stagnates at the stagnation plenum 22.The pressure of the fluid in this stagnation plenum 22 may be measuredby suitable means currently known in the art. Vents 21 and 41 are on theside of the catcher tube 32 and connected directly to ambient pressure.A portion of the fluid travelling through linear resistor 30 ventsitself to ambient through these vents 21 and 41. The pressure at theoutput port 22 is directly proportional to the square of the pressure atthe input port 20.

As can be seen in FIG. 1c the length of the capillary is approximately200 times its thickness L. Moreover, its width is approximately 24 timesits thickness, 24L. Continuing, the output vents are approximately 12L.The catcher tube 32 has a width of approximately 2L.

The central principal axis of the vents are located approximately 16Lfrom the central principal axis of the catcher tube 32 and approximately12L behind the plane of the mouth or opening 31 of the catcher tube 32.

- In FIG. 1d, curve A is an actual plot of P (the output pressure),versus P (the input pressure), of the pure fluid passive square functiongenerator as shown in FIG. lb and FIG. 1c.

It is to be understood that the inventor does not desire to be limitedto the exact detail of construction shown and described for obviousmodifications will occur to a person skilled in the art pertaininghereto.

What is claimed is:

1. A passive fluidic function generator for generating an outputpressure signal which is proportionally related to the square of aninput pressure signal, said generator comprising in combination; inputport means for connection to an input fluid pressure signal source;linear fluidic resistor means connected to said input port means fortransmitting a pressure signal therethrough; a fluidic catcher means forcatching and receiving the pressure signal as it exits said linearfluidic resistor means, said linear fluidic resistor means beingconnected directly to said fluidic catcher means to form a passage ofuniform cross-section between said input port means and said fluidiccatcher means; at least one vent to the ambient disposed between saidfluidic resistor means and said catcher means; means defining a fluidicstagnation plenum connected to said catcher means for stagnating thepressure signal exiting said linear fluidic resistor means; and anoutput port means coupled to said stagnation plenum means for providingan output pressure signal, said output pressure signal beingfunctionally related to the square of the input pressure signal.

2. The function generator of claim 1 wherein said resistor means is acapillary tube.

3. The function generator of claim 2 wherein said tube has a thicknessL, a width 24L, and a length ZOOL.

4. The function generator of claim 3 wherein the input port means tosaid capillary and said vents each have a radius 12L.

5. The function generator of claim 4 wherein said catcher means has awidth 2L and a thickness L.

6. The function generator of claim 2, wherein two vents to ambient areprovided at the end of said capillary one located on each side of saidcatcher.

1. A passive fluidic function generator for generating an outputpressure signal which is proportionally related to the square of aninput pressure signal, said generator comprising in combination; inputport means for connection to an input fluid pressure signal source;linear fluidic resistor means connected to said input port means fortransmitting a pressure signal therethrough; a fluidic catcher means forcatching and receiving the pressure signal as it exits said linearfluidic resistor means, said linear fluidic resistor means beingconnected directly to said fluidic catcher means to form a passage ofuniform cross-section between said input port means and said fluidiccatcher means; at least one vent to the ambient disposed between saidfluidic resistor means and said catcher means; means defining a fluidicstagnation plenum connected to said catcher means for stagnating thepressure signal exiting said linear fluidic resistor means; and anoutput port means coupled to said stagnation plenum means for providingan output pressure signal, said output pressure signal beingfunctionally related to the square of the input pressure signal.
 2. Thefunction generator of claim 1 wherein said resistor means is a capillarytube.
 3. The function generator of claim 2 wherein said tube has athickness L, a width 24L, and a length 200L.
 4. The function generatorof claim 3 wherein the input port means to said capillary and said ventseach have a radius 12L.
 5. The function generator of claim 4 whereinsaid catcher means has a width 2L and a thickness L.
 6. The functiongenerator of claim 2, wherein two vents to ambient are provided at theend of said capillary one located on each side of said catcher.